Problem: What number makes this equation true? $872 + $
Solution: $872 + {{?}} = 981$ ${872}$ ${981}$ $+?$ Let's start by adding hundreds to ${872}$ until we get as close to ${981}$ as possible without going over ${981}$. $\begin{aligned} {872} +100}=972 \end{aligned}$ If we add $1 \text{ hundred}}$, or $1 00}$, we reach $972$. We cannot add any more hundreds without going over ${981}$. ${872}$ ${981}$ ${972}$ $+100$ Next, let's add tens to $972$ until we get as close to ${981}$ as possible without going over ${981}$. We cannot add any tens without going over ${981}$. Finally, how many ones should we add to $972$ to get to ${981}?$ $\begin{aligned} 972+{8} &=980\\\\ 980+{1} &=981 \end{aligned}$ We add ${9\text{ ones}}$. ${872}$ ${981}$ ${972}$ $+100$ $+9$ We added $1 \text{ hundred}}$ and ${9\text{ ones}}$ to ${872}$ to get to ${981}$. $1 00}+{9}={109}$ ${872}$ ${981}$ ${972}$ $+100$ $+9$ $+109$ $872 +{109}= 981$